Answer:
[tex]y = \frac{5}{4} x - 1[/tex]
Step-by-step explanation:
The equation of a line is usually written in the form of y=mx+c, where m is its gradient and c is its y-intercept.
First rewrite the equation of the given line in the form of y=mx +c.
4x+5y=25
5y= -4x +25
[tex]y = - \frac{4}{5} x + 5[/tex]
The gradient of the given line is [tex] - \frac{4}{5} [/tex]
The product of the gradient of perpendicular lines is -1.
[tex]( - \frac{4}{5} )(gradient \: of \: line) = - 1 \\ gradient \: of \: line = - 1 \div ( - \frac{4}{5} ) \\ gradient \: of \: line = \frac{5}{4} [/tex]
Thus, m= [tex] \frac{5}{4} [/tex]
[tex]y = \frac{5}{4} x + c[/tex]
Substitute a coordinate to find c.
When x= -4, y= -6,
[tex] - 6 = \frac{5}{4} ( - 4) + c \\ - 6 = - 5 + c \\ c = 5 - 6 \\ c = - 1[/tex]
Hence, the equation of the line is
[tex]y = \frac{5}{4} x - 1[/tex]
